The invention is related to a fuel injection pump as described by the preamble to the main claim. In a known fuel injection of this type, the pressure variation which is characteristic for the onset of injection is effected by means of engine characteristics, which has particular advantages in the case of starting an internal combustion engine when it is cold. A variation of the external air pressure is well-known to involve substantial difficulties in meeting the increasingly stringent requirements for substantially nontoxic exhaust gas, and these difficulties cannot be solved with the known means of pump control.